Full row/column rank matrices

[kakila]

Hi,
I couldn't find any other way to communicate with the authors of the book. Please excuse me for using this way.
Also I couldn't find an errata for the book, which i think it would be great to have in the website of the book.
My observation here is that the use of full column rank in the book, pp. 16 are not correct. A shirt-fat matrix cannot have full column rank by definition. Since rank(A) <= min(n,m) and in this case n<<m, the rank is at most n, which is the row rank. So a short-fat matrix is likely to have full row rank, not full column rank (number of linearly independent columns equals number of columns), as stated in the book.
In the same page it is also said that a tall-skinny matrix cannot have full column rank, when indeed this is the likely scenario.
I suspect that the authors are using a non-conventional definition of full column rank that they forgot to define.
The conventional definition is intuitive and consistent: column rank == number of linearly independent columns, hence full column rank means all columns are linearly independent.

Regards

[eigensteve]

Thanks Juan Pablo — this is a really good catch! I actually just fixed this for the second edition of the book, so hopefully it is right soon. Thanks for the note, and please feel free to send me any other comments/typos directly. Best wishes, Steve

…

On Sep 13, 2021, at 5:35 PM, Juan Pablo Carbajal ***@***.***> wrote: Hi, I couldn't find any other way to communicate with the authors of the book. Please excuse me for using this way. Also I couldn't find an errata for the book, which i think it would be great to have in the website of the book. My observation here is that the use of full column rank in the book, pp. 16 are not correct. A shirt-fat matrix cannot have full column rank by definition. Since rank(A) <= min(n,m) and in this case n<<m, the rank is at most n, which is the row rank. So a short-fat matrix is likely to have full row rank, not full column rank (number of linearly independent columns equals number of columns), as stated in the book. In the same page it is also said that a tall-skinny matrix cannot have full column rank, when indeed this is the likely scenario. I suspect that the authors are using a non-conventional definition of full column rank that they forgot to define. The conventional definition is intuitive and consistent: column rank == number of linearly independent columns, hence full column rank means all columns are linearly independent. Regards — You are receiving this because you are subscribed to this thread. Reply to this email directly, view it on GitHub <#2>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACCWSUHGCT6AGFRO3MYE3PDUB2KENANCNFSM5D67AM7Q>. Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>.

[kakila]

Hi Steve, I bought my personal copy of the book, it is massive, very nice piece of hard work. I am particularly interested in coarse graining and MOR in complex systems. That part of the book has very good references. In general I would have like to see more GNU Octave next to MATLAB, maybe that's something to consider. BTW, are you planning to host an errata on the book website? Many books do this, it is useful for the owner of older editions, like me, because one can print it and attach it to the book. Congratulations again for the book. Bests, JPi

…

On Tue, Sep 14, 2021, 05:10 Steve Brunton ***@***.***> wrote: Thanks Juan Pablo — this is a really good catch! I actually just fixed this for the second edition of the book, so hopefully it is right soon. Thanks for the note, and please feel free to send me any other comments/typos directly. Best wishes, Steve > On Sep 13, 2021, at 5:35 PM, Juan Pablo Carbajal ***@***.***> wrote: > > > Hi, > I couldn't find any other way to communicate with the authors of the book. Please excuse me for using this way. > Also I couldn't find an errata for the book, which i think it would be great to have in the website of the book. > My observation here is that the use of full column rank in the book, pp. 16 are not correct. A shirt-fat matrix cannot have full column rank by definition. Since rank(A) <= min(n,m) and in this case n<<m, the rank is at most n, which is the row rank. So a short-fat matrix is likely to have full row rank, not full column rank (number of linearly independent columns equals number of columns), as stated in the book. > In the same page it is also said that a tall-skinny matrix cannot have full column rank, when indeed this is the likely scenario. > I suspect that the authors are using a non-conventional definition of full column rank that they forgot to define. > The conventional definition is intuitive and consistent: column rank == number of linearly independent columns, hence full column rank means all columns are linearly independent. > > Regards > > — > You are receiving this because you are subscribed to this thread. > Reply to this email directly, view it on GitHub < #2>, or unsubscribe < https://github.com/notifications/unsubscribe-auth/ACCWSUHGCT6AGFRO3MYE3PDUB2KENANCNFSM5D67AM7Q >. > Triage notifications on the go with GitHub Mobile for iOS < https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android < https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>. > — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub <#2 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AAU62BZRWIASIAILO7VNAF3UB24KZANCNFSM5D67AM7Q> . Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>.

[eigensteve]

Hi JPi, Thanks for the suggestion. We will see what we can do, and ideally will start posting errata on the book website. Best, Steve

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On Sep 14, 2021, at 10:51 AM, Juan Pablo Carbajal ***@***.***> wrote: Hi Steve, I bought my personal copy of the book, it is massive, very nice piece of hard work. I am particularly interested in coarse graining and MOR in complex systems. That part of the book has very good references. In general I would have like to see more GNU Octave next to MATLAB, maybe that's something to consider. BTW, are you planning to host an errata on the book website? Many books do this, it is useful for the owner of older editions, like me, because one can print it and attach it to the book. Congratulations again for the book. Bests, JPi On Tue, Sep 14, 2021, 05:10 Steve Brunton ***@***.***> wrote: > Thanks Juan Pablo — this is a really good catch! I actually just fixed > this for the second edition of the book, so hopefully it is right soon. > Thanks for the note, and please feel free to send me any other > comments/typos directly. > > Best wishes, > Steve > > > On Sep 13, 2021, at 5:35 PM, Juan Pablo Carbajal ***@***.***> wrote: > > > > > > Hi, > > I couldn't find any other way to communicate with the authors of the > book. Please excuse me for using this way. > > Also I couldn't find an errata for the book, which i think it would be > great to have in the website of the book. > > My observation here is that the use of full column rank in the book, pp. > 16 are not correct. A shirt-fat matrix cannot have full column rank by > definition. Since rank(A) <= min(n,m) and in this case n<<m, the rank is at > most n, which is the row rank. So a short-fat matrix is likely to have full > row rank, not full column rank (number of linearly independent columns > equals number of columns), as stated in the book. > > In the same page it is also said that a tall-skinny matrix cannot have > full column rank, when indeed this is the likely scenario. > > I suspect that the authors are using a non-conventional definition of > full column rank that they forgot to define. > > The conventional definition is intuitive and consistent: column rank == > number of linearly independent columns, hence full column rank means all > columns are linearly independent. > > > > Regards > > > > — > > You are receiving this because you are subscribed to this thread. > > Reply to this email directly, view it on GitHub < > #2>, or unsubscribe < > https://github.com/notifications/unsubscribe-auth/ACCWSUHGCT6AGFRO3MYE3PDUB2KENANCNFSM5D67AM7Q > >. > > Triage notifications on the go with GitHub Mobile for iOS < > https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> > or Android < > https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>. > > > > > — > You are receiving this because you authored the thread. > Reply to this email directly, view it on GitHub > <#2 (comment)>, > or unsubscribe > <https://github.com/notifications/unsubscribe-auth/AAU62BZRWIASIAILO7VNAF3UB24KZANCNFSM5D67AM7Q> > . > Triage notifications on the go with GitHub Mobile for iOS > <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> > or Android > <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>. > > — You are receiving this because you commented. Reply to this email directly, view it on GitHub <#2 (comment)>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/ACCWSUBPKFDOI6T3QV7WUILUB6DRBANCNFSM5D67AM7Q>. Triage notifications on the go with GitHub Mobile for iOS <https://apps.apple.com/app/apple-store/id1477376905?ct=notification-email&mt=8&pt=524675> or Android <https://play.google.com/store/apps/details?id=com.github.android&referrer=utm_campaign%3Dnotification-email%26utm_medium%3Demail%26utm_source%3Dgithub>.